catrigl.c revision 1.1.2.2
1 1.1.2.2 pgoyette /* $NetBSD: catrigl.c,v 1.1.2.2 2016/11/04 14:48:54 pgoyette Exp $ */ 2 1.1.2.2 pgoyette /*- 3 1.1.2.2 pgoyette * Copyright (c) 2012 Stephen Montgomery-Smith <stephen (at) FreeBSD.ORG> 4 1.1.2.2 pgoyette * All rights reserved. 5 1.1.2.2 pgoyette * 6 1.1.2.2 pgoyette * Redistribution and use in source and binary forms, with or without 7 1.1.2.2 pgoyette * modification, are permitted provided that the following conditions 8 1.1.2.2 pgoyette * are met: 9 1.1.2.2 pgoyette * 1. Redistributions of source code must retain the above copyright 10 1.1.2.2 pgoyette * notice, this list of conditions and the following disclaimer. 11 1.1.2.2 pgoyette * 2. Redistributions in binary form must reproduce the above copyright 12 1.1.2.2 pgoyette * notice, this list of conditions and the following disclaimer in the 13 1.1.2.2 pgoyette * documentation and/or other materials provided with the distribution. 14 1.1.2.2 pgoyette * 15 1.1.2.2 pgoyette * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 16 1.1.2.2 pgoyette * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 17 1.1.2.2 pgoyette * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 18 1.1.2.2 pgoyette * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 19 1.1.2.2 pgoyette * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 20 1.1.2.2 pgoyette * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 21 1.1.2.2 pgoyette * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 22 1.1.2.2 pgoyette * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 23 1.1.2.2 pgoyette * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 24 1.1.2.2 pgoyette * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 25 1.1.2.2 pgoyette * SUCH DAMAGE. 26 1.1.2.2 pgoyette */ 27 1.1.2.2 pgoyette 28 1.1.2.2 pgoyette /* 29 1.1.2.2 pgoyette * The algorithm is very close to that in "Implementing the complex arcsine 30 1.1.2.2 pgoyette * and arccosine functions using exception handling" by T. E. Hull, Thomas F. 31 1.1.2.2 pgoyette * Fairgrieve, and Ping Tak Peter Tang, published in ACM Transactions on 32 1.1.2.2 pgoyette * Mathematical Software, Volume 23 Issue 3, 1997, Pages 299-335, 33 1.1.2.2 pgoyette * http://dl.acm.org/citation.cfm?id=275324. 34 1.1.2.2 pgoyette * 35 1.1.2.2 pgoyette * The code for catrig.c contains complete comments. 36 1.1.2.2 pgoyette */ 37 1.1.2.2 pgoyette #include <sys/cdefs.h> 38 1.1.2.2 pgoyette __RCSID("$NetBSD: catrigl.c,v 1.1.2.2 2016/11/04 14:48:54 pgoyette Exp $"); 39 1.1.2.2 pgoyette 40 1.1.2.2 pgoyette #include "namespace.h" 41 1.1.2.2 pgoyette #ifdef __weak_alias 42 1.1.2.2 pgoyette __weak_alias(casinl, _casinl) 43 1.1.2.2 pgoyette #endif 44 1.1.2.2 pgoyette #ifdef __weak_alias 45 1.1.2.2 pgoyette __weak_alias(catanl, _catanl) 46 1.1.2.2 pgoyette #endif 47 1.1.2.2 pgoyette 48 1.1.2.2 pgoyette 49 1.1.2.2 pgoyette #include <complex.h> 50 1.1.2.2 pgoyette #include <float.h> 51 1.1.2.2 pgoyette #ifdef __HAVE_LONG_DOUBLE 52 1.1.2.2 pgoyette 53 1.1.2.2 pgoyette #include "math.h" 54 1.1.2.2 pgoyette #include "math_private.h" 55 1.1.2.2 pgoyette 56 1.1.2.2 pgoyette #undef isinf 57 1.1.2.2 pgoyette #define isinf(x) (fabsl(x) == INFINITY) 58 1.1.2.2 pgoyette #undef isnan 59 1.1.2.2 pgoyette #define isnan(x) ((x) != (x)) 60 1.1.2.2 pgoyette #define raise_inexact() do { volatile float junk __unused = /*LINTED*/1 + tiny; } while(/*CONSTCOND*/0) 61 1.1.2.2 pgoyette #undef signbit 62 1.1.2.2 pgoyette #define signbit(x) (__builtin_signbitl(x)) 63 1.1.2.2 pgoyette 64 1.1.2.2 pgoyette #if __HAVE_LONG_DOUBLE + 0 == 128 65 1.1.2.2 pgoyette // Ok 66 1.1.2.2 pgoyette #elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384 67 1.1.2.2 pgoyette // XXX: Byte order 68 1.1.2.2 pgoyette struct ieee_ext { 69 1.1.2.2 pgoyette uint64_t ext_frac; 70 1.1.2.2 pgoyette uint16_t ext_exp:15; 71 1.1.2.2 pgoyette uint16_t ext_sign:1; 72 1.1.2.2 pgoyette uint16_t ext_pad; 73 1.1.2.2 pgoyette }; 74 1.1.2.2 pgoyette #define extu_exp extu_ext.ext_exp 75 1.1.2.2 pgoyette #define extu_sign extu_ext.ext_sign 76 1.1.2.2 pgoyette #define extu_frac extu_ext.ext_frac 77 1.1.2.2 pgoyette union ieee_ext_u { 78 1.1.2.2 pgoyette long double extu_ld; 79 1.1.2.2 pgoyette struct ieee_ext extu_ext; 80 1.1.2.2 pgoyette }; 81 1.1.2.2 pgoyette #else 82 1.1.2.2 pgoyette #error "unsupported long double format" 83 1.1.2.2 pgoyette #endif 84 1.1.2.2 pgoyette 85 1.1.2.2 pgoyette #define GET_LDBL_EXPSIGN(r, s) \ 86 1.1.2.2 pgoyette do { \ 87 1.1.2.2 pgoyette union ieee_ext_u u; \ 88 1.1.2.2 pgoyette u.extu_ld = s; \ 89 1.1.2.2 pgoyette r = u.extu_sign; \ 90 1.1.2.2 pgoyette r >>= EXT_EXPBITS - 1; 91 1.1.2.2 pgoyette } while (/*CONSTCOND*/0) 92 1.1.2.2 pgoyette #define SET_LDBL_EXPSIGN(r, s) \ 93 1.1.2.2 pgoyette do { \ 94 1.1.2.2 pgoyette union ieee_ext_u u; \ 95 1.1.2.2 pgoyette u.extu_ld = s; \ 96 1.1.2.2 pgoyette u.extu_exp &= __BITS(0, EXT_EXPBITS - 1); \ 97 1.1.2.2 pgoyette u.extu_exp |= r << (EXT_EXPBITS - 1); \ 98 1.1.2.2 pgoyette s = u.extu_ld; \ 99 1.1.2.2 pgoyette } while (/*CONSTCOND*/0) 100 1.1.2.2 pgoyette 101 1.1.2.2 pgoyette static const long double 102 1.1.2.2 pgoyette A_crossover = 10, 103 1.1.2.2 pgoyette B_crossover = 0.6417, 104 1.1.2.2 pgoyette FOUR_SQRT_MIN = 0x1p-8189L, 105 1.1.2.2 pgoyette QUARTER_SQRT_MAX = 0x1p8189L, 106 1.1.2.2 pgoyette RECIP_EPSILON = 1/LDBL_EPSILON, 107 1.1.2.2 pgoyette SQRT_MIN = 0x1p-8191L; 108 1.1.2.2 pgoyette 109 1.1.2.2 pgoyette static const long double 110 1.1.2.2 pgoyette m_e = 2.71828182845904523536028747135266250e0L, /* 0x15bf0a8b1457695355fb8ac404e7a.0p-111 */ 111 1.1.2.2 pgoyette m_ln2 = 6.93147180559945309417232121458176568e-1L, /* 0x162e42fefa39ef35793c7673007e6.0p-113 */ 112 1.1.2.2 pgoyette pio2_hi = 1.5707963267948966192313216916397514L, /* pi/2 */ 113 1.1.2.2 pgoyette SQRT_3_EPSILON = 2.40370335797945490975336727199878124e-17L, /* 0x1bb67ae8584caa73b25742d7078b8.0p-168 */ 114 1.1.2.2 pgoyette SQRT_6_EPSILON = 3.39934988877629587239082586223300391e-17L; /* 0x13988e1409212e7d0321914321a55.0p-167 */ 115 1.1.2.2 pgoyette 116 1.1.2.2 pgoyette static const volatile double 117 1.1.2.2 pgoyette pio2_lo = 6.1232339957367659e-17; /* 0x11a62633145c07.0p-106 */ 118 1.1.2.2 pgoyette static const volatile float 119 1.1.2.2 pgoyette tiny = 0x1p-100; 120 1.1.2.2 pgoyette 121 1.1.2.2 pgoyette static long double complex clog_for_large_values(long double complex z); 122 1.1.2.2 pgoyette 123 1.1.2.2 pgoyette inline static long double 124 1.1.2.2 pgoyette f(long double a, long double b, long double hypot_a_b) 125 1.1.2.2 pgoyette { 126 1.1.2.2 pgoyette if (b < 0) 127 1.1.2.2 pgoyette return ((hypot_a_b - b) / 2); 128 1.1.2.2 pgoyette if (b == 0) 129 1.1.2.2 pgoyette return (a / 2); 130 1.1.2.2 pgoyette return (a * a / (hypot_a_b + b) / 2); 131 1.1.2.2 pgoyette } 132 1.1.2.2 pgoyette 133 1.1.2.2 pgoyette inline static void 134 1.1.2.2 pgoyette do_hard_work(long double x, long double y, long double *rx, int *B_is_usable, long double *B, long double *sqrt_A2my2, long double *new_y) 135 1.1.2.2 pgoyette { 136 1.1.2.2 pgoyette long double R, S, A; 137 1.1.2.2 pgoyette long double Am1, Amy; 138 1.1.2.2 pgoyette 139 1.1.2.2 pgoyette R = hypotl(x, y+1); 140 1.1.2.2 pgoyette S = hypotl(x, y-1); 141 1.1.2.2 pgoyette 142 1.1.2.2 pgoyette A = (R + S) / 2; 143 1.1.2.2 pgoyette if (A < 1) 144 1.1.2.2 pgoyette A = 1; 145 1.1.2.2 pgoyette 146 1.1.2.2 pgoyette if (A < A_crossover) { 147 1.1.2.2 pgoyette if (y == 1 && x < LDBL_EPSILON*LDBL_EPSILON/128) { 148 1.1.2.2 pgoyette *rx = sqrtl(x); 149 1.1.2.2 pgoyette } else if (x >= LDBL_EPSILON * fabsl(y-1)) { 150 1.1.2.2 pgoyette Am1 = f(x, 1+y, R) + f(x, 1-y, S); 151 1.1.2.2 pgoyette *rx = log1pl(Am1 + sqrtl(Am1*(A+1))); 152 1.1.2.2 pgoyette } else if (y < 1) { 153 1.1.2.2 pgoyette *rx = x/sqrtl((1-y)*(1+y)); 154 1.1.2.2 pgoyette } else { 155 1.1.2.2 pgoyette *rx = log1pl((y-1) + sqrtl((y-1)*(y+1))); 156 1.1.2.2 pgoyette } 157 1.1.2.2 pgoyette } else 158 1.1.2.2 pgoyette *rx = logl(A + sqrtl(A*A-1)); 159 1.1.2.2 pgoyette 160 1.1.2.2 pgoyette *new_y = y; 161 1.1.2.2 pgoyette 162 1.1.2.2 pgoyette if (y < FOUR_SQRT_MIN) { 163 1.1.2.2 pgoyette *B_is_usable = 0; 164 1.1.2.2 pgoyette *sqrt_A2my2 = A * (2 / LDBL_EPSILON); 165 1.1.2.2 pgoyette *new_y= y * (2 / LDBL_EPSILON); 166 1.1.2.2 pgoyette return; 167 1.1.2.2 pgoyette } 168 1.1.2.2 pgoyette 169 1.1.2.2 pgoyette *B = y/A; 170 1.1.2.2 pgoyette *B_is_usable = 1; 171 1.1.2.2 pgoyette 172 1.1.2.2 pgoyette if (*B > B_crossover) { 173 1.1.2.2 pgoyette *B_is_usable = 0; 174 1.1.2.2 pgoyette if (y == 1 && x < LDBL_EPSILON/128) { 175 1.1.2.2 pgoyette *sqrt_A2my2 = sqrtl(x)*sqrtl((A+y)/2); 176 1.1.2.2 pgoyette } else if (x >= LDBL_EPSILON * fabsl(y-1)) { 177 1.1.2.2 pgoyette Amy = f(x, y+1, R) + f(x, y-1, S); 178 1.1.2.2 pgoyette *sqrt_A2my2 = sqrtl(Amy*(A+y)); 179 1.1.2.2 pgoyette } else if (y > 1) { 180 1.1.2.2 pgoyette *sqrt_A2my2 = x * (4/LDBL_EPSILON/LDBL_EPSILON) * y / 181 1.1.2.2 pgoyette sqrtl((y+1)*(y-1)); 182 1.1.2.2 pgoyette *new_y = y * (4/LDBL_EPSILON/LDBL_EPSILON); 183 1.1.2.2 pgoyette } else { 184 1.1.2.2 pgoyette *sqrt_A2my2 = sqrtl((1-y)*(1+y)); 185 1.1.2.2 pgoyette } 186 1.1.2.2 pgoyette } 187 1.1.2.2 pgoyette } 188 1.1.2.2 pgoyette 189 1.1.2.2 pgoyette long double complex 190 1.1.2.2 pgoyette casinhl(long double complex z) 191 1.1.2.2 pgoyette { 192 1.1.2.2 pgoyette long double x, y, ax, ay, rx, ry, B, sqrt_A2my2, new_y; 193 1.1.2.2 pgoyette int B_is_usable; 194 1.1.2.2 pgoyette long double complex w; 195 1.1.2.2 pgoyette 196 1.1.2.2 pgoyette x = creall(z); 197 1.1.2.2 pgoyette y = cimagl(z); 198 1.1.2.2 pgoyette ax = fabsl(x); 199 1.1.2.2 pgoyette ay = fabsl(y); 200 1.1.2.2 pgoyette 201 1.1.2.2 pgoyette if (isnan(x) || isnan(y)) { 202 1.1.2.2 pgoyette if (isinf(x)) 203 1.1.2.2 pgoyette return (CMPLXL(x, y+y)); 204 1.1.2.2 pgoyette if (isinf(y)) 205 1.1.2.2 pgoyette return (CMPLXL(y, x+x)); 206 1.1.2.2 pgoyette if (y == 0) return (CMPLXL(x+x, y)); 207 1.1.2.2 pgoyette return (CMPLXL(x+0.0L+(y+0), x+0.0L+(y+0))); 208 1.1.2.2 pgoyette } 209 1.1.2.2 pgoyette 210 1.1.2.2 pgoyette if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { 211 1.1.2.2 pgoyette if (signbit(x) == 0) 212 1.1.2.2 pgoyette w = clog_for_large_values(z) + m_ln2; 213 1.1.2.2 pgoyette else 214 1.1.2.2 pgoyette w = clog_for_large_values(-z) + m_ln2; 215 1.1.2.2 pgoyette return (CMPLXL(copysignl(creall(w), x), copysignl(cimagl(w), y))); 216 1.1.2.2 pgoyette } 217 1.1.2.2 pgoyette 218 1.1.2.2 pgoyette if (x == 0 && y == 0) 219 1.1.2.2 pgoyette return (z); 220 1.1.2.2 pgoyette 221 1.1.2.2 pgoyette raise_inexact(); 222 1.1.2.2 pgoyette 223 1.1.2.2 pgoyette if (ax < SQRT_6_EPSILON/4 && ay < SQRT_6_EPSILON/4) 224 1.1.2.2 pgoyette return (z); 225 1.1.2.2 pgoyette 226 1.1.2.2 pgoyette do_hard_work(ax, ay, &rx, &B_is_usable, &B, &sqrt_A2my2, &new_y); 227 1.1.2.2 pgoyette if (B_is_usable) 228 1.1.2.2 pgoyette ry = asinl(B); 229 1.1.2.2 pgoyette else 230 1.1.2.2 pgoyette ry = atan2l(new_y, sqrt_A2my2); 231 1.1.2.2 pgoyette return (CMPLXL(copysignl(rx, x), copysignl(ry, y))); 232 1.1.2.2 pgoyette } 233 1.1.2.2 pgoyette 234 1.1.2.2 pgoyette long double complex 235 1.1.2.2 pgoyette casinl(long double complex z) 236 1.1.2.2 pgoyette { 237 1.1.2.2 pgoyette long double complex w = casinhl(CMPLXL(cimagl(z), creall(z))); 238 1.1.2.2 pgoyette return (CMPLXL(cimagl(w), creall(w))); 239 1.1.2.2 pgoyette } 240 1.1.2.2 pgoyette 241 1.1.2.2 pgoyette long double complex 242 1.1.2.2 pgoyette cacosl(long double complex z) 243 1.1.2.2 pgoyette { 244 1.1.2.2 pgoyette long double x, y, ax, ay, rx, ry, B, sqrt_A2mx2, new_x; 245 1.1.2.2 pgoyette int sx, sy; 246 1.1.2.2 pgoyette int B_is_usable; 247 1.1.2.2 pgoyette long double complex w; 248 1.1.2.2 pgoyette 249 1.1.2.2 pgoyette x = creall(z); 250 1.1.2.2 pgoyette y = cimagl(z); 251 1.1.2.2 pgoyette sx = signbit(x); 252 1.1.2.2 pgoyette sy = signbit(y); 253 1.1.2.2 pgoyette ax = fabsl(x); 254 1.1.2.2 pgoyette ay = fabsl(y); 255 1.1.2.2 pgoyette 256 1.1.2.2 pgoyette if (isnan(x) || isnan(y)) { 257 1.1.2.2 pgoyette if (isinf(x)) 258 1.1.2.2 pgoyette return (CMPLXL(y+y, -INFINITY)); 259 1.1.2.2 pgoyette if (isinf(y)) 260 1.1.2.2 pgoyette return (CMPLXL(x+x, -y)); 261 1.1.2.2 pgoyette if (x == 0) return (CMPLXL(pio2_hi + pio2_lo, y+y)); 262 1.1.2.2 pgoyette return (CMPLXL(x+0.0L+(y+0), x+0.0L+(y+0))); 263 1.1.2.2 pgoyette } 264 1.1.2.2 pgoyette 265 1.1.2.2 pgoyette if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) { 266 1.1.2.2 pgoyette w = clog_for_large_values(z); 267 1.1.2.2 pgoyette rx = fabsl(cimagl(w)); 268 1.1.2.2 pgoyette ry = creall(w) + m_ln2; 269 1.1.2.2 pgoyette if (sy == 0) 270 1.1.2.2 pgoyette ry = -ry; 271 1.1.2.2 pgoyette return (CMPLXL(rx, ry)); 272 1.1.2.2 pgoyette } 273 1.1.2.2 pgoyette 274 1.1.2.2 pgoyette if (x == 1 && y == 0) 275 1.1.2.2 pgoyette return (CMPLXL(0, -y)); 276 1.1.2.2 pgoyette 277 1.1.2.2 pgoyette raise_inexact(); 278 1.1.2.2 pgoyette 279 1.1.2.2 pgoyette if (ax < SQRT_6_EPSILON/4 && ay < SQRT_6_EPSILON/4) 280 1.1.2.2 pgoyette return (CMPLXL(pio2_hi - (x - pio2_lo), -y)); 281 1.1.2.2 pgoyette 282 1.1.2.2 pgoyette do_hard_work(ay, ax, &ry, &B_is_usable, &B, &sqrt_A2mx2, &new_x); 283 1.1.2.2 pgoyette if (B_is_usable) { 284 1.1.2.2 pgoyette if (sx==0) 285 1.1.2.2 pgoyette rx = acosl(B); 286 1.1.2.2 pgoyette else 287 1.1.2.2 pgoyette rx = acosl(-B); 288 1.1.2.2 pgoyette } else { 289 1.1.2.2 pgoyette if (sx==0) 290 1.1.2.2 pgoyette rx = atan2l(sqrt_A2mx2, new_x); 291 1.1.2.2 pgoyette else 292 1.1.2.2 pgoyette rx = atan2l(sqrt_A2mx2, -new_x); 293 1.1.2.2 pgoyette } 294 1.1.2.2 pgoyette if (sy==0) 295 1.1.2.2 pgoyette ry = -ry; 296 1.1.2.2 pgoyette return (CMPLXL(rx, ry)); 297 1.1.2.2 pgoyette } 298 1.1.2.2 pgoyette 299 1.1.2.2 pgoyette long double complex 300 1.1.2.2 pgoyette cacoshl(long double complex z) 301 1.1.2.2 pgoyette { 302 1.1.2.2 pgoyette long double complex w; 303 1.1.2.2 pgoyette long double rx, ry; 304 1.1.2.2 pgoyette 305 1.1.2.2 pgoyette w = cacosl(z); 306 1.1.2.2 pgoyette rx = creall(w); 307 1.1.2.2 pgoyette ry = cimagl(w); 308 1.1.2.2 pgoyette if (isnan(rx) && isnan(ry)) 309 1.1.2.2 pgoyette return (CMPLXL(ry, rx)); 310 1.1.2.2 pgoyette if (isnan(rx)) 311 1.1.2.2 pgoyette return (CMPLXL(fabsl(ry), rx)); 312 1.1.2.2 pgoyette if (isnan(ry)) 313 1.1.2.2 pgoyette return (CMPLXL(ry, ry)); 314 1.1.2.2 pgoyette return (CMPLXL(fabsl(ry), copysignl(rx, cimagl(z)))); 315 1.1.2.2 pgoyette } 316 1.1.2.2 pgoyette 317 1.1.2.2 pgoyette static long double complex 318 1.1.2.2 pgoyette clog_for_large_values(long double complex z) 319 1.1.2.2 pgoyette { 320 1.1.2.2 pgoyette long double x, y; 321 1.1.2.2 pgoyette long double ax, ay, t; 322 1.1.2.2 pgoyette 323 1.1.2.2 pgoyette x = creall(z); 324 1.1.2.2 pgoyette y = cimagl(z); 325 1.1.2.2 pgoyette ax = fabsl(x); 326 1.1.2.2 pgoyette ay = fabsl(y); 327 1.1.2.2 pgoyette if (ax < ay) { 328 1.1.2.2 pgoyette t = ax; 329 1.1.2.2 pgoyette ax = ay; 330 1.1.2.2 pgoyette ay = t; 331 1.1.2.2 pgoyette } 332 1.1.2.2 pgoyette 333 1.1.2.2 pgoyette if (ax > LDBL_MAX / 2) 334 1.1.2.2 pgoyette return (CMPLXL(logl(hypotl(x / m_e, y / m_e)) + 1, atan2l(y, x))); 335 1.1.2.2 pgoyette 336 1.1.2.2 pgoyette if (ax > QUARTER_SQRT_MAX || ay < SQRT_MIN) 337 1.1.2.2 pgoyette return (CMPLXL(logl(hypotl(x, y)), atan2l(y, x))); 338 1.1.2.2 pgoyette 339 1.1.2.2 pgoyette return (CMPLXL(logl(ax*ax + ay*ay) / 2, atan2l(y, x))); 340 1.1.2.2 pgoyette } 341 1.1.2.2 pgoyette 342 1.1.2.2 pgoyette inline static long double 343 1.1.2.2 pgoyette sum_squares(long double x, long double y) 344 1.1.2.2 pgoyette { 345 1.1.2.2 pgoyette if (y < SQRT_MIN) 346 1.1.2.2 pgoyette return (x*x); 347 1.1.2.2 pgoyette 348 1.1.2.2 pgoyette return (x*x + y*y); 349 1.1.2.2 pgoyette } 350 1.1.2.2 pgoyette 351 1.1.2.2 pgoyette inline static long double 352 1.1.2.2 pgoyette real_part_reciprocal(long double x, long double y) 353 1.1.2.2 pgoyette { 354 1.1.2.2 pgoyette long double scale; 355 1.1.2.2 pgoyette uint16_t hx, hy; 356 1.1.2.2 pgoyette int16_t ix, iy; 357 1.1.2.2 pgoyette 358 1.1.2.2 pgoyette GET_LDBL_EXPSIGN(hx, x); 359 1.1.2.2 pgoyette ix = hx & 0x7fff; 360 1.1.2.2 pgoyette GET_LDBL_EXPSIGN(hy, y); 361 1.1.2.2 pgoyette iy = hy & 0x7fff; 362 1.1.2.2 pgoyette #define BIAS (LDBL_MAX_EXP - 1) 363 1.1.2.2 pgoyette #define CUTOFF (LDBL_MANT_DIG / 2 + 1) 364 1.1.2.2 pgoyette if (ix - iy >= CUTOFF || isinf(x)) 365 1.1.2.2 pgoyette return (1/x); 366 1.1.2.2 pgoyette if (iy - ix >= CUTOFF) 367 1.1.2.2 pgoyette return (x/y/y); 368 1.1.2.2 pgoyette if (ix <= BIAS + LDBL_MAX_EXP / 2 - CUTOFF) 369 1.1.2.2 pgoyette return (x/(x*x + y*y)); 370 1.1.2.2 pgoyette scale = 1; 371 1.1.2.2 pgoyette SET_LDBL_EXPSIGN(scale, 0x7fff - ix); 372 1.1.2.2 pgoyette x *= scale; 373 1.1.2.2 pgoyette y *= scale; 374 1.1.2.2 pgoyette return (x/(x*x + y*y) * scale); 375 1.1.2.2 pgoyette } 376 1.1.2.2 pgoyette 377 1.1.2.2 pgoyette long double complex 378 1.1.2.2 pgoyette catanhl(long double complex z) 379 1.1.2.2 pgoyette { 380 1.1.2.2 pgoyette long double x, y, ax, ay, rx, ry; 381 1.1.2.2 pgoyette 382 1.1.2.2 pgoyette x = creall(z); 383 1.1.2.2 pgoyette y = cimagl(z); 384 1.1.2.2 pgoyette ax = fabsl(x); 385 1.1.2.2 pgoyette ay = fabsl(y); 386 1.1.2.2 pgoyette 387 1.1.2.2 pgoyette if (y == 0 && ax <= 1) 388 1.1.2.2 pgoyette return (CMPLXL(atanhl(x), y)); /* XXX need atanhl() */ 389 1.1.2.2 pgoyette 390 1.1.2.2 pgoyette if (x == 0) 391 1.1.2.2 pgoyette return (CMPLXL(x, atanl(y))); 392 1.1.2.2 pgoyette 393 1.1.2.2 pgoyette if (isnan(x) || isnan(y)) { 394 1.1.2.2 pgoyette if (isinf(x)) 395 1.1.2.2 pgoyette return (CMPLXL(copysignl(0, x), y+y)); 396 1.1.2.2 pgoyette if (isinf(y)) 397 1.1.2.2 pgoyette return (CMPLXL(copysignl(0, x), copysignl(pio2_hi + pio2_lo, y))); 398 1.1.2.2 pgoyette return (CMPLXL(x+0.0L+(y+0), x+0.0L+(y+0))); 399 1.1.2.2 pgoyette } 400 1.1.2.2 pgoyette 401 1.1.2.2 pgoyette if (ax > RECIP_EPSILON || ay > RECIP_EPSILON) 402 1.1.2.2 pgoyette return (CMPLXL(real_part_reciprocal(x, y), copysignl(pio2_hi + pio2_lo, y))); 403 1.1.2.2 pgoyette 404 1.1.2.2 pgoyette if (ax < SQRT_3_EPSILON/2 && ay < SQRT_3_EPSILON/2) { 405 1.1.2.2 pgoyette raise_inexact(); 406 1.1.2.2 pgoyette return (z); 407 1.1.2.2 pgoyette } 408 1.1.2.2 pgoyette 409 1.1.2.2 pgoyette if (ax == 1 && ay < LDBL_EPSILON) { 410 1.1.2.2 pgoyette #if 0 411 1.1.2.2 pgoyette if (ay > 2*LDBL_MIN) 412 1.1.2.2 pgoyette rx = - logl(ay/2) / 2; 413 1.1.2.2 pgoyette else 414 1.1.2.2 pgoyette #endif 415 1.1.2.2 pgoyette rx = - (logl(ay) - m_ln2) / 2; 416 1.1.2.2 pgoyette } else 417 1.1.2.2 pgoyette rx = log1pl(4*ax / sum_squares(ax-1, ay)) / 4; 418 1.1.2.2 pgoyette 419 1.1.2.2 pgoyette if (ax == 1) 420 1.1.2.2 pgoyette ry = atan2l(2, -ay) / 2; 421 1.1.2.2 pgoyette else if (ay < LDBL_EPSILON) 422 1.1.2.2 pgoyette ry = atan2l(2*ay, (1-ax)*(1+ax)) / 2; 423 1.1.2.2 pgoyette else 424 1.1.2.2 pgoyette ry = atan2l(2*ay, (1-ax)*(1+ax) - ay*ay) / 2; 425 1.1.2.2 pgoyette 426 1.1.2.2 pgoyette return (CMPLXL(copysignl(rx, x), copysignl(ry, y))); 427 1.1.2.2 pgoyette } 428 1.1.2.2 pgoyette 429 1.1.2.2 pgoyette long double complex 430 1.1.2.2 pgoyette catanl(long double complex z) 431 1.1.2.2 pgoyette { 432 1.1.2.2 pgoyette long double complex w = catanhl(CMPLXL(cimagl(z), creall(z))); 433 1.1.2.2 pgoyette return (CMPLXL(cimagl(w), creall(w))); 434 1.1.2.2 pgoyette } 435 1.1.2.2 pgoyette 436 1.1.2.2 pgoyette #else 437 1.1.2.2 pgoyette __strong_alias(_casinl, casin) 438 1.1.2.2 pgoyette __strong_alias(_catanl, catan) 439 1.1.2.2 pgoyette __strong_alias(cacoshl, cacosh) 440 1.1.2.2 pgoyette __strong_alias(cacosl, cacos) 441 1.1.2.2 pgoyette __strong_alias(casinhl, casinh) 442 1.1.2.2 pgoyette __strong_alias(catanhl, catanh) 443 1.1.2.2 pgoyette #endif 444
Indexes created Tue Oct 14 15:09:51 GMT 2025